Certificate for #16367 ⟨a, b | aba=aa, babb=ab⟩

Back:⟨a, b | aba=aa, babb=ab⟩

Completion settings:

[1] aba=aa

Axiom: aba=aa.

Defines rule #1.

Referenced by [3], [4], [5].

[2] babb=ab

Axiom: babb=ab.

Defines rule #5.

Referenced by [3], [4].

[3] aabb=aab

Overlap of [1] aba=aa with [2] babb=ab:

a ba babb

Critical pair: aab=aabb.

Flip LHS and RHS.

Defines rule #2.

Referenced by [4].

[4] baab=aab

Overlap of [2] babb=ab with [2] babb=ab:

bab b babb

Critical pair: babab=ababb.

Reduce LHS:

[1]b(aba)b
⇒ baab

Reduce RHS:

[1](aba)bb
[3]⇒ (aabb)
⇒ aab

Defines rule #4.

Referenced by [5].

[5] baaa=aaa

Overlap of [4] baab=aab with [1] aba=aa:

ba ab aba

Critical pair: baaa=aaba.

Reduce RHS:

[1]a(aba)
⇒ aaa

Defines rule #3.